Wednesday, March 20, 2013

Fundamentality and ungroundedness

I haven't been following the grounding literature, so this may be old hat, in which case I will be grateful for references.

The following seems pretty plausible:

p is fundamental if and only if p is ungrounded.

But I think (1) may be false. I will put the argument in tensed fashion, but it could also be done a bit more awkwardly in a four-dimensional setting.

Let's suppose that <I ought to respect other persons> is a fundamental moral truth. Call this truth R. But now I validly promise to respect other persons. Then R comes to be grounded in <I ought to keep my promises and I promised to respect other persons>. If (1) is true, then R continues to be true but ceases to be fundamental. That doesn't sound right. It seems to me that if R is ever a fundamental moral truth, then it is always a fundamental moral truth. After I have promised to respect other persons, R gained a ground but lost nothing of its fundamentality.

Maybe I can motivate my intuition a little more. It seems that R has a relevantly different status from the status had by S, the proposition <I ought to come to your house for dinner every night>, after I promise you to come to your house for dinner every night. Each of R and S is grounded by a proposition about promises, but intuitively the fundamentality-and-grounding statuses of R and S are different. A sign (but only a sign--we want to avoid the conditional fallacy) of the difference is that R would still be true were the proposition about promises false. Another sign of the difference is that <I ought to respect you> is overdeterminingly grounded in <I ought to respect all persons> and <I promised to respect all persons and I ought to keep my promises>, while it is false that <I ought to come for dinner tomorrow night> is overdeterminingly grounded in <I ought to come for dinner every night> and <I promised to come for dinner every night and I ought to keep my promises>. The latter is not a case of overdetermination.

The above example is controversial, and I can't think of any noncontroversial ones. But it seems plausible that we should be open to phenomena like the above. Such prima facie possibilities suggest to me that ungroundedness is a negative property, while fundamentality is something positive. Normally, fundamental truths are also ungrounded. But they don't lose their fundamentality if in some world they happen to be grounded as well.

A somewhat tempting way to keep the above intuition while maintaining the idea that fundamentality is to drop the irreflexivity of grounding and say that:

p is fundamental if and only if p grounds p.

Then we could say that R is overdeterminingly grounded by a proposition about promises as well as by R itself, while S is only grounded by a proposition about promises and not by S. And in ordinary language we do sometimes use expressions like "p because p" to express some kind of fundamentality of p. I am not that happy with this solution, but can't think of another one that keeps the idea that fundamentality is defined in terms of grounding. Of course, one could take fundamentality to be fundamental.

22 comments:

Interesting post! Perhaps we also get cases like this with instances of the law of excluded middle. Suppose P is a contingent proposition. There is some intuitive plausibility to the claim that [P or ~P] is fundamental; it's a basic truth of logic, after all. But it's typically held that disjunctions are grounded in their true disjuncts. If both of these claims are correct, then [P or ~P] will be both fundamental and grounded in whichever of its disjuncts is true.Another possible case comes from fundamental laws of nature. Suppose it's a fundamental law that all Fs are G. Then, plausibly, [All Fs are G] is fundamental. But it's also typically held that universal truths of this form are grounded in their instances ([o1 is G], [o2 is G],...), together with a suitable totality fact ([o1, o2,... are all the Fs]). Suppose that o is F (and so G). Then [All Fs are G] will be both fundamental and (partially) grounded in [o is G].

Excluded middle and other instances of fundamental axiom schemata may be a good example.

I am not convinced by the law of nature case, first because I am sceptical that universal truths are grounded in their instances (universal truths seem to me to be negative claims), and second because I don't think fundamental laws are fundamental truths. It might be on some account of laws that if L is a fundamental law, then it's a fundamental truth that L is a law. But that doesn't make L itself be a fundamental truth.

Some more cases.

1. Maybe <Possibly there are exactly five photons> is fundamental. But in the world where there are exactly five photons, it's also grounded in <There are five photons.>

2. Maybe Molinist conditionals are fundamental. But <C→E> will be grounded in <C> and <E> in worlds where both C and E hold. Does the conditional stop being fundamental there?

On the other hand, there is this worry. Maybe <I ought to A> should be seen as a disjunction: <I fundamentally-ought to A or I derivatively-ought to A>. So it's never ungrounded, because it is always grounded at least in the first disjunct, and perhaps in both. And promising doesn't make the first disjunct true.

Then one better then hope that "fundamentally-ought" isn't defined in terms of "is fundamental".

Perhaps the term 'ungrounded' in 1. is ambiguous, at least in light of the example that you give. It seems to me that "I ought to respect other persons" can be a fundamental moral truth with respect to a moral epistemology but grounded in "I ought to keep my promises and I promised to respect other persons" in a different way. Specifically, it seems that this second proposition expresses a grounding for the motivation to act in conformity with 1.

The problem with 2. is that it is consistent with come fundamental interpretation in which 1. is also true (that there is some ultimate notion of "fundamental").

Why should we think that R comes to be grounded in a duty to keep promises after I promise it? Here's my initial thought: I may gain a reason why I should respect persons when I so promise, but the most basic fact remains that I should respect them. It may even be that the reason I ought to keep promises is because I ought to respect persons (or some such suitably nuanced theory).

Jonathon's point is what I immediately think of in your first example. You call it "overdetermination", and I think it shows that "I ought to respect other persons" is utterly independent of "I promised to respect you, and I should keep my promises". It is not any more true or binding, and therefore remains wholly ungrounded by S.

I also strongly disagree that, with fundamental truths, "p grounds p". I think it's logically incoherent for p to ground p. For p to ground q seems to me to mean the following:

1) If p is false, then either q should be rejected or it has some other ground. 2) If p is true, then we have reason to think q is true.

But, if p could ground p, it translates to:

3) If p is false, then either we have reason to reject p, or else p has some other ground.4) If p is true, then we have reason to think p is true.

Neither 3 nor 4 seem to give what we intuitively mean by "ground".

In any case, my point is that your (1) is correct, and fundamental truths are ungrounded. This is the meaning of "fundamental" in every context where we use the term.

I disagree with your first example, about the LEM. As an axiom, the LEM is just telling us that it is never the case that both P and ~P are both false. It doesn't derive its truth from the actual truth value of either disjunct, but sets an axiomatic rule that it will never be the case that P↓~P.

Alex,

To your two subsequent cases:

1. Possibly there are exactly 5 photons doesn't seem like a fundamental truth. There isn't anything grounded on it, nor is there any necessity to its truth. But, even if it is fundamental, the presence of 5 actual photons wouldn't change that fundamental truth in the slightest. I mean, you can deduce the possibility of 5 photons from its actuality (isn't that Brower's Axiom?... in any case, it seems obvious). But, if it is a fundamental truth that there possibly exist 5 photons, then the actuality of it doesn't increase or ground or in any way affect that fundamental truth.

2. Again, if a Molinist conditional is fundamental, then it is necessarily true, and cannot be grounded in the instantiation of the conjuncts in a possible world.

One more point: Consider your original example. You have two fundamental truths: {I should respect other people} and {I should keep my promises}. Now, the statement {I should respect Sally, whom I promised to respect} has double grounding in these fundamental truths. But the two fundamental truths are never involved in grounding each other.

I was wondering if I could ask a question related to your new book rather than to one regarding this specific blog post.

I am actually just a lay Christian; I'm not a philosopher. But I would imagine that you wrote One Body with the broad Body of Christ in mind, so I feel okay asking this. Just bare my lack of philosophical specialization in mind :).

My question is on your view on masturbatory activity. You think it wrong given that it is not directed towards the good that you have identified. But isn't it the case that folks can get prostate cancer if semen is not regularly emitted? Thus, wouldn't it be the case that a good towards which masturbation is directed would be to avoid cancer? For single folks, I mean. I suppose that this might depend upon how prone one may be towards getting something like prostate cancer and so maybe such an activity would be okay for such individuals?

It's wrong because it produces an illusion of love's union, without the reality of love's union. And love is too great a thing to be deceived about.

The medical data on masturbation and prostate cancer is complicated. Masturbation in younger men is associated with a significant increase in prostate cancer risk, and in older men with a significant decrease. Here's some information. In any case, the fact that something might have some medical benefit doesn't make it right. Stealing money for a medical treatment is immoral, but it might have medical benefits.

If I promise to God to eat no animals, then <I should eat no animals> comes to be true, and true with a ground. Likewise if I promise to God to respect all persons, then while <I should respect all persons> doesn't come to be true, as it already was, it should at least gain a ground. No?

Jon Kvanvig suggested an interesting move to me: maybe one can say that this is a case like overdetermination, and David Lewis said that overdeterminers aren't causes. Maybe likewise they're not grounds.

I really like Kvanvig's point, and it's kind of what I was getting at. If something is already fundamental, then it is axiomatically true. Promising to uphold a fundamental ethic does not seem to ground that ethic in the promise. I think we should be careful about what we call "fundamental" (for example, is keeping promises fundamentally good, or is it grounded in our respect for other people?), but I think that when we truly have fundamentals, they cannot gain or lose grounding.

To look at from the other direction, imagine if someone discharged you from your promise to respect people. Has the fundamental truth "you should respect others" lost anything? It doesn't seem so.

On the other hand, suppose I promise one of my kids to take all my kids to the zoo. The proposition <I should take all my kids to the zoo> comes to be true and grounded. I then issue the same promise to another one of my kids. The proposition doesn't lose the grounding it previously had, but it certainly gains another.

Likewise, if I promise to do something that was independently a duty, the proposition that I ought to do it gains a new grounding. If it had no grounding, it comes to have one. If it had one grounding, it comes to have two.

The analogue to the Lewis point about overdetermination is typically rejected in the grounding literature. It is generally accepted that <p or q> is grounded in <p> whenever <p> is true, and is grounded in <q> whenever <q> is true. So when both are true, it is grounded in each.

John Giannini just suggested to me that my grounding graph approach might be helpful here (I am linking to my earlier version of the approach as it's more helpful in this context).

Just drop the Absoluteness of Fundamentality axiom in the linked-to post. Now, a proposition is defined in the post as fundamental provided it is initial in some grounding graph. Our proposition R has two grounding pathways. One of them goes through propositions about promises. The other makes R fundamental.

However, I think one also needs to drop Noncircularity. For the duty to keep promises might in turn be grounded in the duty to respect persons.

One of the things that I've noticed about the different examples given here (especially the one in the original post) is that they are unqualifiedly fundamental entities. To be fundamental is to be not grounded by anything period. So, a moral truth like what you give in your example would usually be taken to be grounded in something else like the natures of certain concreta or the creators commands or how it relates to the overall value of reality, etc.

I would imagine that the same would go for facts about possibility. All facts about possibility would be grounded in some recombinatorial principle or something like that.

My point is that all of the candidates given as being fundamental seem that they are not fundamental simpliciter but are fundamental with respect to a certain ontological category or something else but would then go on to be grounded in some entity (or entities) in some different ontological category or whatnot. So, it seems that what you need to get the result you want is an example of something that is unqualifiedly fundamental that could be grounded in something else.

Maybe one way to go about it is to say that there is a world W where the mereological simples are not the mereological simples in another world W' but some smaller things are the simples in W'. So, say the atoms in this world are as small as you get in W but in W' you bottom out at protons, neutrons, and electrons. So in W atoms make a good candidate for something that is fundamental in an unqualified sense (by being the basic building blocks of concrete reality) but in W' would be grounded in something else.

The suggestion to use contingent simples is pretty neat, but I doubt there are any.I meant my examples to be of things that on a not crazy theory are fundamental. Maybe they're not really fundamental, but I don't think the theory of fundamentality should rule such cases out.

I agree that a theory of fundamentality shouldn't rule out things like that from the start, but I worry that since, after theorizing many philosophers haven't seem to have taken moral facts or modal facts as fundamental, that your examples would just further entrench that those kinds of entities or facts aren't fundamental. So, I guess I'm curious if there are any less controversial candidates for fundamentality that you could re-run the considerations made in post with. (Also, out of curiosity, why think that there wouldn't be contingent simples?)

I really like the idea that fundamentality and grounding can come apart. Like, I really like the idea that something like biological things or persons could be grounded in smaller material things but are still are fundamental entities.

I don't know that the ethics examples are all that controversial. I think many non-Aristotelian naturalist moral realists will say that some ethical truths are fundamental truths.

The modality example is also not that far off from views that people hold. A lot of Platonists hold that some propositions have a fundamental property of necessity. Why wouldn't some do it with possibility, too? At least, we shouldn't rule that out on the basis of a definition of fundamentality.

Along the lines of Brian's law of nature suggestion, if you accept that universally quantified claims are grounded in their instances, you might also note that All bachelors are unmarried seems to be both fundamental and grounded.

Well, my problem wasn't with non-fundamentals being grounded twice, it was with the idea that a fundamental truth could gain extra grounding via some contingent circumstance relative to another fundamental truth. That's what I think is problematic. So, if my duty to respect others is fundamental, then that cannot be increased by a promise I make to God that I will respect others. I do not have any more grounding for that fundamental requirement than I already did.

If taking one's children to the zoo were itself a fundamental good, it wouldn't become any more grounded if you promised them to do so. You are just promising them to do that which you are morally enjoined to do anyway. Now, there may be more accountability in the latter case (viz, your children will be even more upset and lose faith in you), but it doesn't seem that the fundamental requirement has taken on any further grounding.

1) Calling a moral proposition "fundamental" seems to entail necessity. If there are necessary moral truths, then they hold (at least as counter-factuals) in every possible world. So, the only way to have a contingent fundamental ethic is to have one that conforms to all the others, but is not grounded in any of them. That doesn't just seem unlikely, but also seems to mean that there are substantial, salient gaps in the ones that are necessary, and that these gaps will manifest in the possible worlds which lack the contingent fundamentals in question.

2) With regard to Brian's point, it seems to me that universally quantified propositions are grounded in either some fundamental truth or their instances, but not both. After all, if we had some non-inductive knowledge (perhaps even a priori)) that all X's are Y, then it would add absolutely nothing in terms of grounding, for us to look around and inductively notice that all X's are Y.

3) Something I implied in the previous post, but want to state more clearly: It seems to me that there is an essential difference between an instance of application of an ethical principle, and the ethic principle itself. I don't necessary mean that these principles are abstracta that get instantiated (though that's one way to look at it), but I just mean that there's the principle itself on the one hand, and there's an instance of following the principle on another. An instance of behaving a particular way can have several groundings, and that is not problematic. But that is rather different from the grounding of the guiding principles themselves. For example, "I should keep my promises to my wife" is grounded in the more fundamental principle that I should keep all promises (and perhaps also in the principle that one should treat one's spouse with thoughtful respect). It is not itself a fundamental principle. However, if the principle "I should keep all promises" is fundamental, then it is unchanged by the fact that this particular person is my wife.

I don't know if I'm expressing my thought clearly, but I hope you get the picture. Basically: An instance of behaving morally can have lots of groundings. The principles guiding moral behavior can also have many groundings. But the most fundamental principles are essentially un-grounded. They are themselves the "ground level", so to speak, and that a building is built on two adjacent plots of ground does not mean that either of the two plots is itself built on the other plot.

Here's a different problem with the moral case. There are different kinds of moral duty connected to different kinds of ground. Thus, there are promise-based duties, command-based duties, etc. And more finely: promise-to-x-based duties, command-by-y-based-duties, etc. But if that's right, then maybe there are also fundamental-duties. And if so, then what I should say is that <I ought to respect others> is grounded in both <I have a fundamental duty to respect others> and <I have a promise-based duty to respect others>. And the argument now fails. For the promise-based duty doesn't ground the fundamental-duty.

This sort of distinction helps capture why it is doubly wrong to break a promise to two people. For then I have two duties to A, a duty-to-x to A and a duty-to-y to A. And if A'ing is fundamentally required, then I also have a fundamental-duty to A.

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